A lot of scientists and engineers face the limitation of tools like Matlab and Mathematica.
So slow but has a great advantage of easy to formulate the mathematical theory and easy to plot.

When I first introduced several colleagues the advantages of Java languages. They responses always like this ... I know but I could not afford to learn another big language like Java. And the biggest problem is not easy to formulate the mathematical idea into Java code and I don't know where to start graphical plots of my results.

Here is the remedy for those.

Most of scientific and mathematics will be covered by these libraries
1. Jscience
2. JFormula

Graphical plots (almost easy as Matlab/Mathematica)
1. JFreeChart
2. JGraph

Special research supports (Bioinformatics, Machine Learning)
1. biojava
2. weka

All other answers can be found in Java.net

Goodbye, Matlab / Mathematica ~

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